In this paper we give the étale local classification of Schelter-Procesi smooth orders in central simple algebras. In particular, we prove that if is a central simple -algebra of dimension , where is a field of trancendence degree , then there are only finitely many étale local classes of smooth orders in . This result is a non-commutative generalization of the fact that a smooth variety is analytically a manifold, and so has only one type of étale local behaviour.